Diagnosis of Balanced Vortex Structure Using Potential Vorticity

Abstract

A useful set of equations with which to describe tropical cyclones in gradient wind balance involves using the total flow for advection. Transformation of these equations to angular momentum coordinates has advantages including simplification of the advection terms and -stretching of regions of large vorticity. The resulting equation set is a generalization of the two-dimensional semigeostrophic approximation to curved flows. A method for the integration of this equation set is described in this paper and is shown to be analogous to the semigeostrophic case. The potential vorticity equation plays a central role and in the presence of diabatic sources and sinks a large variation in potential vorticity across the vortex will develop. The equation set can be integrated in time once a convective parameterization scheme is specified linking the diabatic term to the explicit motion. The structure of balanced vortices is described for plausible boundary variations of potential temperature and interior variations in potential vorticity. This involves the numerical solution of the nonlinear elliptic equation for the modified geopotential function. This study, while pertaining only to ?snapshot? vortex states, provides a basis for a time integration of the full problem with convective parameterization and gives dynamical insight into vortex structure. Horizontal variations of potential vorticity due to a sloping tropopause and due to diabatic forcing in the tropospheric core region are shown to have a major effect on vortex structure analogous to that of boundary variations of temperature. Increased surface temperature, a lower tropopause, or larger tropospheric potential vorticity in the core are all consistent with cyclonic circulation. Furthermore, the static stability is strongly affected and there are situations with low values in the core consistent with the possibility of enhanced convection.